A. 11.1
B. 6.7
C. 13
D. 4.1

Answers

Answer 1

Answer:

Answer:

C.13

LineAE&LineADhavethesameinmeasurement.

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What is the similarity ratio of the smaller to the larger prisms? Enter your answer as a:b

Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

Answers

Answer:

r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x 2 − 5 ) , ( 0 , − 2 ) (devil's curve) y2(y2-4)=x2(x2-5), (0,-2) (devil's curve)

Answers

Answer:

y = -2

Step-by-step explanation:

To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx

The equation is

$y^2(y^2-4)=x^2(x^2-5)$

implicit differentiation give us

$(d)/(dx)[y^2(y^2-4)=x^2(x^2-5)]\n\n2y(dy)/(dx)(y^2-4)+y^2(2y(dy)/(dx))=2x(x^2-5)+x^2(2x)\n\n4y^3(dy)/(dx)-8y(dy)/(dx)=2x^3-10x+2x^3\n\n(dy)/(dx)=(4x^3-10x)/(4y^3-8y)$

But we know that

$m=(dy)/(dx)\ny=mx+b$

Hence, for the point (0,-2) and by replacing for dy/dx

$m=(dy)/(dx)_((0,-2))=(4(0)+10(0))/(4(-2)^3-8(-2))=0$

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:

y=(0)x+b = -2

HOPE THIS HELPS!!

In order to find the equation of the tangent line to the curve y²(y² - 4) = x²(x² - 5) at the point (0, -2), we will use the method of implicit differentiation. Here are the steps:

Step 1: Differentiate Each Side of the Given Equation with Respect to x

Applying the chain rule to differentiate y²(y² - 4) with respect to x gives:
2y*y'(y² - 4) + y²*2y*y' = d/dx [y²(y² - 4)]
The chain rule is also applied to differentiate x²(x² - 5) with respect to x, yielding:
2x(x² - 5) + x²*2x = d/dx [x²(x² - 5)]

Step 2: Equate the Two Expressions Found from Step 1 and Solve for y'

2y*y'(y² - 4) + y²*2y*y' = 2x(x² - 5) + x²*2x

This equation can be solved by isolating y' (the derivative of y with respect to x), which represents the slope of the tangent line.

Step 3: Use the Given Point (0, -2) to Find the Slope of the Tangent Line

Substitute x = 0 and y = -2 into the equation found in Step 2 to get the specific value for the slope at the given point.

Step 4: Use the Point-Slope Form of the Line to Write the Equation of the Tangent Line

The point-slope form of the line y - y₁ = m(x - x₁) can be used to write the equation of the tangent line. We substitute for x₁ and y₁ with the coordinates of the given point (0, -2), and m with the slope found from Step 3.

The resulting equation represents the tangent line to the curve at the given point (0, -2). Please note that the full calculation may result in a complex slope due to the nature of the given curve equation. Nonetheless, this process illustrates the application of implicit differentiation and the point-slope form of a line in finding the equation of a tangent line to a curve.

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Niccola travels at an average speed of 40 mph for 50 miles.Without stopping, Niccola then travels 60 miles in 1.75 hours.
Find her average speed for the entire journey to 2 dp.

Answers

Answer:

Step-by-step explanation:

I am sorry i need points, i cant

You have 8 quarts of brown stock. You need 3 cups to make one serving of braised short ribs. How many servings can you make? (don't include partial portions)

Answers

Answer:

You can make 2 servings.

Step-by-step explanation:

Hi there!

3 cups makes one serving, so 2 servings require 6 cups. Since you don't have 9 cups to make 3 servings, and you don't want partial portions, you can only make 2 servings with 6 cups and have 2 cups left over.

Have a great day!

(I'd also appreicate it if I got a rating and maybe a Thanks please!)

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.) My Notes Ask Your Teacher (a) the volume of the cube maximum possible error relative error percentage error cm
(b) the surface area of the cube maximum possible error relative error percentage error cm Need Help? ReadTalk to Tuter

Answers

Answer with Step-by-step explanation:

We are given that

Side of cube, x=30 cm

Error in measurement of edge, $\delta x=0.5$ cm

(a)

Volume of cube, $V=x^3$

Using differential

$dV=3x^2dx$

Substitute the values

$dV=3(30)^2(0.5)$

$dV=1350 cm^3$

Hence, the maximum possible error in computing the volume of the cube

= $1350 cm^3$

Volume of cube, $V=(30)^3=27000 cm^3$

Relative error= $(dV)/(V)=(1350)/(2700)$

Relative error=0.05

Percentage error= $0.05* 100=5$ %

Hence, relative error in computing the volume of the cube=0.05 and

percentage error in computing the volume of the cube=5%

(b)

Surface area of cube, $A=6x^2$

$dA=12xdx$

$dA=12(30)(0.5)$

$dA=180cm^2$

The maximum possible error in computing the volume of the cube= $180cm^2$

$A=6(30)^2=5400cm^2$

Relative error= $(dA)/(A)=(180)/(5400)$

Relative error in computing the volume of the cube=0.033

The percentage error in computing the volume of the cube= $0.033* 100=3.3$ %

Out of the 800 students enrolled in a recreationalflag-football program, 32% are seventh graders.
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graders?

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